Weekly Math Updates

December 20, 2006

Contents:

Christmas Message

District Finishes Math Rubric

In God We Trust Donations

Comic Contest

Dan Olsen's Math Article

Media Articles

Weekly Comic

Christmas Message

We all have a lot to be thankful for this Christmas. Not only are we blessed to have children to be concerned over, but we have had the blessing of improving their lot in life by working at improving their future educational experience. The gift of a good education is something that can't be understated, and it helps those most who could least afford to do without it.

I hope you'll permit me to share a little Christmas thought. Most often in our lives we don't know when God has reached out and blessed us. It requires a moment of self-reflection each day to look back on the experiences we've had and try to recognize those experiences that blessed our life that day. The easiest type of blessing to recognize is when someone else has done something for us to lift our burden and lighten our load just a little.

It seems to me the great test of life is two-fold: First, recognizing God's hand in our lives; and second, in being God's hand in others' lives. Sometimes it's through our conscientious decision to reach out in service to someone else in their trials and afflictions that those people come to realize God's hand is in their life. Some people never recognize it without the influence of another providing that act of kindness.

During this Christmas season, I hope each of us will reflect on our blessings and commit to do something good for someone that is unable to lift their life's load. That single act of charity may have an effect more far reaching than you will ever see in this life, but perhaps through the eternities you will be gratified beyond measure for the ripple effect of your small effort. As King Benjamin said in the Book of Mormon, "when ye are in the service of your fellow beings, ye are only in the service of your God."

District Finishes Math Rubric

I received a copy of the district's "rubric" (spec sheet) this week to be used in selection of the math programs to let each school choose to use. It's a combination of constructivism and instructivism. The sad thing is, they've developed this and it's going to be meaningless come late Spring when the new Utah math standards are completed. ASD might as well toss darts at a board if they're not going to wait for the standards to pick the programs from...unless they pick really strong programs like California has done.

In God We Trust Donations

I would like to thank those of you that made additional donations last week. One individual donated $100 alone. What greater gift can we give our children than to learn "In God We Trust" is our daily motto? So many people don't understand that message.

We still need just over $1,100 to ensure all the classrooms in the district have a poster. If you can spare even $5 to help put a few signs up in Alpine School District, please donate today. $5 puts up 10 posters. If you can spare $25, that would help an entire school have posters. For just $25 you can help positively influence hundreds of students on a daily basis. Think of the hundreds of dollars you're saving in tutoring and supplementation in the future because of the improvements we've made to math in our district. Click this link to donate now:

There won't be an email next week but for the following week, I will send a free copy of Ozzie (the 2nd best word game ever) to the person who comes up with the best caption for a New Year's resolution comic. Hit reply to this email to send it to me and if for some reason it doesn't go through, just use the "contact me" form on my website.

Dan Olsen's Math Article

“Math facts” vs. “Problem solving”

As a professor of computer science and as a father, I have watched the math debate for many years. One of my concerns is the polarization between “math facts” and “problem solving”. Both of these positions are wrong and both of them are right.

What our children need to be successful in the technology and math-based economy of the future is the ability to look at a problem in the world, develop a symbolic or logical representation of that problem and then derive a solution from that representation. Those are a lot of big words for the goal. More simply it is the ability to accurately and rapidly solve “word problems” of increasing complexity.

No computer scientist ever does long division on other than trivial problems. We all use calculators. However, that does not mean that math facts and long division should be purged from the curriculum. When I teach introduction to programming we use programs that are trivial and irrelevant because they a simple enough to teach and practice fundamental concepts. Add-with-carry and long division are simple algorithms that can be taught to children. By repeatedly working these problems and learning to manipulate symbols, children gain skills and ways of thinking that will be needed later. It is the practice with algorithms that is so crucial. Practice, practice, practice.

Students who have such skills can easily learn to program, build bridges or design automobiles. Students who have be taught to “draw pictures of the problem until they feel good about the result” or “design your own way to think about this problem” are being cheated. They are bogged down trying to discover “trivialities” so that they never acquire the tools needed to discover really important things.

Problem solving skill is critical in a technological world. Great problem solvers have at their command many tools and techniques. They also have the ability to look at the world and rapidly chose from those tools. They have at their finger tips the solutions discovered by those who have gone before and are prepared to apply them in new ways. Great painters first master the color, brush technique, lighting, perspective and composition of past masters. Then with these tools they express themselves in new ways. Great art is founded on the prior mastery of great technique. Great technology is founded on the prior mastery of numbers and algorithms.

Forcing students to wander in an aimless “journey of investigation” does not make them great problem solvers. It cripples them by forcing them to discover 18th century mathematics in a 21st century world. It teaches them to “guess at answers” and “search for the magic trick” rather than apply well practiced tools to achieve solid solutions. The goal of education is to help students avoid the numerous dead ends already explored by those who have gone before. Newton, Gauss, Leibniz and many others have already labored to produce techniques that provide problem-solving power. We should pass these tools on to our children rather than force them to rediscover them.

Mathematics can provide exact answers to many real problems, not just fuzzy good feelings about those problems. Math facts and long division are a sandbox in which children develop skills before they face more difficult algorithms. Math facts alone, however, are not sufficient. Repeated and continuous skill practice with word problems is also essential. A student must translate the world to mathematics and then mathematics to a solution. Both skills are exact, disciplined and essential. This should be the heart of a mathematics curriculum. The artificial debate about calculators vs. times tables vs. problem solving is irrelevant.

"The leadership of each institution has to make improvement a priority for it to work. Successful organizations have long learned that what the "boss" says is what gets done. So, unless presidents of each institution "walk the walk" and create a culture of expectations, nothing will happen."

Glasnost, Perestroika and Graphing Calculators (by John Dewey)http://www.edspresso.com/2006/12/glasnost_perestroika_and_graph.htm
This latest article by John Dewey illustrates what drives me nuts more than anything. We criticize constructivists for dumbing down our kids and not teaching them the foundational tenets of math, and then if we use anything close to what they're using as an illustration or to start to lay the foundation with a very simple example, they start touting we're coming to their side of the aisle. Dear constructivists, got news for you, we've been using that for years. We just didn't stop at first base with our students and we got them home by teaching them the rest of the principles.